The Sweden u-21 international has made five appearances for the Red Devils since making his debut towards the end of last season.
He scored his first goal for the club in the Premier League against Wolverhampton Wanderers on the last day of last season.
The 19-year-old joined Manchester United’s academy at the age of 12.
'My ultimate ambition has always been to play for Manchester United. The standard is extremely high, but this contract is another important moment in my journey,’ Elanga told Manchester United’s official website.
'This is the perfect environment to take the next step, with world-class players and coaches to learn from every day.
'I am overjoyed that the Club has shown such faith in my development, and I want to thank my family and all of the staff for their ongoing support.
'I know that with hard-work and dedication comes opportunity at this special club and I cannot wait to continue my progress here. Glory to God always.'
Football director John Murtough added: 'Anthony is a young player that we all really believe in. He has consistently impressed throughout the Academy age groups and risen to every challenge that he has faced.
'Anthony is extremely dedicated; he has the work-rate and attitude to keep improving every day and succeed at Manchester United. He is yet another fantastic example of the type of player that our world-leading youth development system continues to produce.
'We are thrilled that Anthony has signed this new contract, and everyone is excited to see him grow over the coming seasons.'